30,436 research outputs found
Consensus on Nonlinear Spaces
peer reviewedConsensus problems have attracted significant attention in the control community
over the last decade. They act as a rich source of new mathematical problems pertaining to
the growing field of cooperative and distributed control. This paper is an introduction to
consensus problems whose underlying state-space is not a linear space, but instead a highly
symmetric nonlinear space such as the circle and other relevant generalizations. A geometric
approach is shown to highlight the connection between several fundamental models of consensus,
synchronization, and coordination, to raise significant global convergence issues not present in
linear models, and to be relevant for a number of engineering applications, including the design
of planar or spatial coordinated motions
Distributed Adaptive Learning with Multiple Kernels in Diffusion Networks
We propose an adaptive scheme for distributed learning of nonlinear functions
by a network of nodes. The proposed algorithm consists of a local adaptation
stage utilizing multiple kernels with projections onto hyperslabs and a
diffusion stage to achieve consensus on the estimates over the whole network.
Multiple kernels are incorporated to enhance the approximation of functions
with several high and low frequency components common in practical scenarios.
We provide a thorough convergence analysis of the proposed scheme based on the
metric of the Cartesian product of multiple reproducing kernel Hilbert spaces.
To this end, we introduce a modified consensus matrix considering this specific
metric and prove its equivalence to the ordinary consensus matrix. Besides, the
use of hyperslabs enables a significant reduction of the computational demand
with only a minor loss in the performance. Numerical evaluations with synthetic
and real data are conducted showing the efficacy of the proposed algorithm
compared to the state of the art schemes.Comment: Double-column 15 pages, 10 figures, submitted to IEEE Trans. Signal
Processin
Hypergraph conditions for the solvability of the ergodic equation for zero-sum games
The ergodic equation is a basic tool in the study of mean-payoff stochastic
games. Its solvability entails that the mean payoff is independent of the
initial state. Moreover, optimal stationary strategies are readily obtained
from its solution. In this paper, we give a general sufficient condition for
the solvability of the ergodic equation, for a game with finite state space but
arbitrary action spaces. This condition involves a pair of directed hypergraphs
depending only on the ``growth at infinity'' of the Shapley operator of the
game. This refines a recent result of the authors which only applied to games
with bounded payments, as well as earlier nonlinear fixed point results for
order preserving maps, involving graph conditions.Comment: 6 pages, 1 figure, to appear in Proc. 54th IEEE Conference on
Decision and Control (CDC 2015
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